Question

If x^2+1/x^2=27,find the value of x-(1/x) please find the answer as quick as you can.

Answer 1

Answer :

Given that,

$x^{2} + \frac{1}{x^{2}}=27\\ \\\implies {(x - \frac{1}{x} )}^{2} + 2(x)( \frac{1}{x} ) = 27 \\ \\ \implies {(x - \frac{1}{x} )}^{2} = 27 - 2 = 25$

∴ x - $\frac{1}{x}$ = ± 5

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Answer 2

$x^2 + \frac{1}{x^2} = 27 \\ \\ = x^2 + (\frac{1}{x})^2 = 27 \\ \\ \\ x^2 + (\frac{1}{x})^2 - 2 = 27 - 2 \\ \\ = x^2 + \frac{1}{x^2} - (2 \times x \times \frac{1}{x}) = 27 - 2 \\ \\ = x^2 + \frac{1}{x^2} - (2 \times x \times \frac{1}{x}) = 25 \\ \\ = (x - \frac{1}{x})^2 = 25 \\ \\ \\ x - \frac{1}{x} = \sqrt{25} = 5 \\ \\ OR \\ \\ x - \frac{1}{x} = \sqrt{25} = - 5$

5 or -5 is the answer.

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